Hence, the result of [1]} that terminality implies non-signalling follows from our propositions REF  and  together.
Our premise that actions by different local agents commute is weaker than the assumptions employed by [1]}.
In conclusion, our approach strengthens the argument in [1]} for the significance of a condition like terminality.
At the same time, we take a more general approach to subsystems than the bottom-up model of process theories in [1]}, thus highlighting the role of commutation in the context of defining local agents and non-signalling.
